AbstractWave-particle duality has long been treated as an intrinsic property of quantumsystems. This paper proposes a correction to this interpretation. We argue thatduality is not an ontological property of the system itself, but a consequence of themeasurement context.We introduce the Zulfia Equation as a formal framework:Z = η + ∆ (1)where Z denotes the observed state, η denotes the underlying informational invari-ant, and ∆ denotes its contextual manifestation.Within this framework, particle-like and wave-like behaviors are understood asdifferent manifestations (∆) of the same informational substrate (η). We reinterpretquantum tunneling as a case of Information-Faced Tunneling, where η is conservedwhile ∆ is filtered by the potential barrier, offering a consistent resolution to theduality paradox.
AbstractWave-particle duality has long been treated as an intrinsic property of quantumsystems. This paper proposes a correction to this interpretation. We argue thatduality is not an ontological property of the system itself, but a consequence of themeasurement context.We introduce the Zulfia Equation as a formal framework:Z = η + ∆ (1)where Z denotes the observed state, η denotes the underlying informational invari-ant, and ∆ denotes its contextual manifestation.Within this framework, particle-like and wave-like behaviors are understood asdifferent manifestations (∆) of the same informational substrate (η). We reinterpretquantum tunneling as a case of Information-Faced Tunneling, where η is conservedwhile ∆ is filtered by the potential barrier, offering a consistent resolution to theduality paradox.
AbstractThis work re-examines the 1973 concept of quantum tunnelling, historically described asa Magic Tunnelling phenomenon where a particle crosses a barrier without a physicalmechanism. In conventional quantum mechanics, tunnelling is treated as barrier penetrationprobability based on wave leakage, T ∼ e−2kL, without defining what tunnelling is.We introduce a conceptual framework for quantum tunnelling denoted as Z = η + ∆, calledZulfia Mapping. Here η is defined as the discrete, quantal state carrying invariant identityI(η), which cannot travel alone, while ∆ represents the continuous, contextual field of natureand barrier. Wave does not travel alone; it must hold the finger of η.In Z-language, we convert the magic concept into a real concept. Tunnelling is re-definednot as crossing the barrier, but as the formation of a new state Z via η + ∆ → Z, underidentity conservation I(T (η)) = I(η). Thus, the barrier is not an obstacle to be crossed,but a context to meet.Consequently, Z → η1, η2 provides a built-in origin for entanglement, and the observableend-state is defined as the MI Communication State ZM I = ηmessage + ∆channel. This marksthe transition from 1973 Magic Tunnelling to 2026 MI Tunnelling — from magicsafar to MI safari. This formalism provides a foundation for analysing information transferacross physical and natural systems
This preprint presents a field-first interpretation of wave-particle duality grounded in the ontology of Quantum Field Theory (QFT). The framework treats quantum fields as the fundamental ontology of physical reality, while particles are understood as excitation states of their respective fields. Wave-like phenomena, including interference, diffraction, tunneling, and coherence effects, are interpreted as arising from the propagation and interaction dynamics of these excitations rather than from an independent wave ontology. The central thesis is that wave-particle duality does not represent two distinct physical realities, but rather different observational regimes of a single field-based process. Localized interactions appear particle-like, while propagation and interference phenomena appear wave-like. This interpretation is fully consistent with the existing mathematical formalism of Quantum Field Theory and does not introduce new physical laws or modifications to established quantum mechanics. The purpose of this work is interpretive and conceptual. It aims to provide a clearer ontological framework for understanding the relationship between quantum fields, particles, and wave-like behavior while reducing the conceptual ambiguity traditionally associated with wave-particle duality. This document represents the initial preprint release of the field-first interpretation framework.
AbstractThe century-old wave-particle duality posits that quantum objects are either Matter orWave, with transition governed by probability P = |ψ|2. Here we disprove probability asfundamental.We report discovery of a third state of nature, ZMI (Zulfia Mass-Information)State, defined by M I = η + I where η is direction-generated mass and I is information.We show quantum processes are not probabilistic but informational domain transfersgoverned by feasibility Q.Using Python lab-equivalent simulation, validated as table-top STM analogue, wedemonstrate universal triad Matter → Wave → ZMI. Quantum tunnelling is firstexample: Before tunnelling = Wave with Born rule; After Q > 0, W → ZM I withMaf ter = Mbef ore + η. This Maf ter > Mbef ore is smoking gun of ZMI.This establishes W → ZM I as unavoidable, replacing Born probability with Q =Tinto ZM I . Discovery redefines tunnelling from transmission to factory of mass-information.
This work proposes a minimal ontological framework for interpreting wave–particle duality as a boundary-sensitive manifestation of quantum phenomena on an underlying, physically real but unobservable background. Rather than treating wave-like and particle-like behaviors as competing physical entities, the framework interprets them as distinct modes of manifestation determined by global boundary conditions. Motivated by interference experiments such as the double-slit setup, the study argues that experimental outcomes depend on boundary-induced modifications of a background structure beyond the local particle path. Within this view, wave-like interference corresponds to a nonlocal manifestation shaped by boundary conditions, while particle-like detection corresponds to localized manifestation events at measurement. The proposed interpretation preserves the standard quantum formalism while offering a realist, boundary-centered conceptual perspective that avoids observer-dependent collapse or multi-path particle propagation. The manuscript is provided as a preprint to invite open scientific discussion and critical evaluation.
AbstractWe propose a simple projection law Z = η + ∆, where η is existence and ∆ isthe projection or viewing frame. Z is observed reality. We show that what is ofteninterpreted as unification or dualization in physics can be understood as projectioneffects of this law. We re-examine four standard examples:(i) unification of forces (GUT),(ii) dead / living body distinction,(iii) wave-particle duality (double-slit), and(iv) Salam’s electroweak unification.We introduce a falsifiable test - the Zulfia Fist Test: if upon removal of ∆, multipleη or multiple Z reappear, then the original Z was a convergence or divergenceillusion, not a fundamental merger or duality.Keywords: TOEE, Zulfia Law of Existence, Z = η+∆, Unification, Dualization,Projection, Illusion, Evaluation
For more than a century since Schr¨odinger, the quantum wave equation has been as-sumed to hold on a fully accessible domain Ω without certified origin. No extension in theavailable literature has revisited its foundational probability assumption.We replace this assumption with a deviation origin. Using Zulfia Decomposition inProbability (ZDM) Z(t) = MZ [η(t0)] + ∆(t) within Zulfia Bi-Face Probability Theory(ZBPT) [1], the information field after collision is restricted to deviation domain Ω \ ΩC =∆−1(̸= 0) where ∆(t)̸ = 0 where PZ does not exist and C(ω) = 0, with certified domainΩC = ∆−1(0) excluded where ∆(t) = 0.iℏZ CZ (ω) ∂∆(t)∂t = − ℏ2Z2mZ∇ · (CZ (ω)∇∆(t)) + VZ (ω)∆(t) on Ω \ ΩC (1)The conventional equationiℏ∂tψ = − ℏ22m ∇2ψ + V ψ (2)is the special case for Ω \ ΩC ≈ Ω, CZ = 1.After Collision is strictly informational, mass-free on Ω \ ΩC .